Question

Use the information given to enter an equation in standard form.

(−1, 1) and (0, 2) .

Answer 1

First find the slope:

m = ( 2 - 1 ) / ( 0 - (-1) ) = 1 / 1 = 1

Set up slope-intercept form:

y = 1·x +2

Now move x and y to the left and leave 2 on the right:

-x + y = 2

This is also equivalent to x - y = -2, so that just depends if you want your x coefficient to be positive or negative.

Answer 2

Standard form: x - y = -2

Explanation:

The standard form of linear equations is Ax + By = C, where A, B, and C are integers; A and B ≠ 0, and A is a non-negative integer.

Given the two points, we must first solve for the value of the slope.

Let (x₁, y₁) = (-1, 1)

(x₂, y₂) = (0, 2)

Substitute these values into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

m = (2 - 1)/[0 - (-1)]

m = 1/(0 + 1) = 1

Therefore, the value of the slope, m = 1.

Next, we need to determine the y-intercept, which is the point on the graph where it crosses the y-axis. The y-intercept is also the value of y when x = 0. One of the given points happens to be the y-intercept, (0, 2). Its y-coordinate is the value of b in the slope-intercept form, y = mx + b. Substitute the slope and the y-intercept into the equation:

y = mx + b

y = x + 2

Next, we need to rewrite the slope-intercept form into its standard form, Ax + By = C:

y = x + 2

Subtract x from both sides:

- x + y = x - x + 2

-x + y = 2

Multiply both sides of the equation by -1, so that the coefficient of x becomes a positive integer:

(-1) (-x + y) = 2(-1)

x - y = -2 ⇒ This is the standard form where A = 1, B = -1, and C = -2